LMFDB - Embedded newform 1638.2.bj.i.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 $ x^16 - 2x^15 + 2x^14 + 18x^13 + 143x^12 - 148x^11 + 172x^10 + 1612x^9 + 6655x^8 + 478x^7 + 1106x^6 + 11266x^5 + 55249x^4 + 8856x^3 + 288x^2 + 7488*x + 97344
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.3
Root			$2.48294 - 2.48294i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.i.1135.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -0.145508i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -0.145508i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(0.0727538 + 0.126013i) q^{10} +(-1.30736 + 0.754806i) q^{11} +(-2.95619 - 2.06420i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.160487 + 0.277972i) q^{17} +(-1.44811 - 0.836065i) q^{19} +(-0.126013 - 0.0727538i) q^{20} +(0.754806 - 1.30736i) q^{22} +(2.75250 + 4.76747i) q^{23} +4.97883 q^{25} +(3.59224 + 0.309553i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(4.59467 + 7.95821i) q^{29} +0.879471i q^{31} +(0.866025 + 0.500000i) q^{32} -0.320974i q^{34} +(-0.0727538 + 0.126013i) q^{35} +(3.14281 - 1.81450i) q^{37} +1.67213 q^{38} +0.145508 q^{40} +(-1.12780 + 0.651136i) q^{41} +(0.499222 - 0.864677i) q^{43} +1.50961i q^{44} +(-4.76747 - 2.75250i) q^{46} +1.30183i q^{47} +(0.500000 + 0.866025i) q^{49} +(-4.31179 + 2.48941i) q^{50} +(-3.26575 + 1.52804i) q^{52} +5.12731 q^{53} +(0.109830 + 0.190231i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-7.95821 - 4.59467i) q^{58} +(2.78339 + 1.60699i) q^{59} +(1.63869 - 2.83829i) q^{61} +(-0.439735 - 0.761644i) q^{62} -1.00000 q^{64} +(-0.300357 + 0.430148i) q^{65} +(1.99785 - 1.15346i) q^{67} +(0.160487 + 0.277972i) q^{68} -0.145508i q^{70} +(6.10671 + 3.52571i) q^{71} +1.35714i q^{73} +(-1.81450 + 3.14281i) q^{74} +(-1.44811 + 0.836065i) q^{76} +1.50961 q^{77} +8.66217 q^{79} +(-0.126013 + 0.0727538i) q^{80} +(0.651136 - 1.12780i) q^{82} +0.148560i q^{83} +(0.0404470 + 0.0233521i) q^{85} +0.998443i q^{86} +(-0.754806 - 1.30736i) q^{88} +(7.13132 - 4.11727i) q^{89} +(1.52804 + 3.26575i) q^{91} +5.50500 q^{92} +(-0.650914 - 1.12742i) q^{94} +(-0.121654 + 0.210711i) q^{95} +(11.4206 + 6.59366i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 2 q^{10} + 12 q^{11} + 10 q^{13} + 16 q^{14} - 8 q^{16} + 6 q^{17} - 4 q^{22} + 12 q^{23} - 20 q^{25} + 2 q^{26} - 16 q^{29} - 2 q^{35} - 6 q^{37} + 4 q^{40} - 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} + 24 q^{50} - 4 q^{52} + 40 q^{53} + 20 q^{55} + 8 q^{56} + 6 q^{58} - 6 q^{59} - 2 q^{61} + 14 q^{62} - 16 q^{64} + 52 q^{65} - 30 q^{67} - 6 q^{68} - 12 q^{71} - 24 q^{74} - 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} - 30 q^{89} + 4 q^{91} + 24 q^{92} - 8 q^{94} + 40 q^{95} - 24 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^10 + 12 * q^11 + 10 * q^13 + 16 * q^14 - 8 * q^16 + 6 * q^17 - 4 * q^22 + 12 * q^23 - 20 * q^25 + 2 * q^26 - 16 * q^29 - 2 * q^35 - 6 * q^37 + 4 * q^40 - 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 + 24 * q^50 - 4 * q^52 + 40 * q^53 + 20 * q^55 + 8 * q^56 + 6 * q^58 - 6 * q^59 - 2 * q^61 + 14 * q^62 - 16 * q^64 + 52 * q^65 - 30 * q^67 - 6 * q^68 - 12 * q^71 - 24 * q^74 - 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 - 30 * q^89 + 4 * q^91 + 24 * q^92 - 8 * q^94 + 40 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	0.145508i		−	0.0650729i	−0.999471	−	0.0325365i	$-0.989641\pi$
$5$		−	0.145508i		−	0.0650729i	0.999471	−	0.0325365i	$-0.0103585\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.0727538	+	0.126013i	0.0230068	+	0.0398489i
$11$	−1.30736	+	0.754806i	−0.394184	+	0.227582i	−0.683972	−	0.729509i	$-0.739749\pi$
$11$	−1.30736	+	0.754806i	−0.394184	+	0.227582i	0.289787	+	0.957091i	$0.406415\pi$
$12$		0			0
$13$	−2.95619	−	2.06420i	−0.819900	−	0.572506i
$13$	−2.95619	−	2.06420i	−0.819900	−	0.572506i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.160487	+	0.277972i	−0.0389238	+	0.0674180i	−0.884831	−	0.465912i	$-0.845726\pi$
$17$	−0.160487	+	0.277972i	−0.0389238	+	0.0674180i	0.845907	+	0.533330i	$0.179060\pi$
$18$		0			0
$19$	−1.44811	−	0.836065i	−0.332219	−	0.191807i	0.324607	−	0.945849i	$-0.394768\pi$
$19$	−1.44811	−	0.836065i	−0.332219	−	0.191807i	−0.656826	+	0.754042i	$0.728101\pi$
$20$	−0.126013	−	0.0727538i	−0.0281774	−	0.0162682i
$21$		0			0
$22$	0.754806	−	1.30736i	0.160925	−	0.278730i
$23$	2.75250	+	4.76747i	0.573936	+	0.994087i	0.996156	+	0.0875933i	$0.0279176\pi$
$23$	2.75250	+	4.76747i	0.573936	+	0.994087i	−0.422220	+	0.906493i	$0.638749\pi$
$24$		0			0
$25$	4.97883			0.995766
$26$	3.59224	+	0.309553i	0.704496	+	0.0607083i
$27$		0			0
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	4.59467	+	7.95821i	0.853209	+	1.47780i	0.878296	+	0.478117i	$0.158680\pi$
$29$	4.59467	+	7.95821i	0.853209	+	1.47780i	−0.0250870	+	0.999685i	$0.507986\pi$
$30$		0			0
$31$			0.879471i			0.157958i	0.996876	+	0.0789788i	$0.0251659\pi$
$31$			0.879471i			0.157958i	−0.996876	+	0.0789788i	$0.974834\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	0.320974i		−	0.0550466i
$35$	−0.0727538	+	0.126013i	−0.0122976	+	0.0213001i
$36$		0			0
$37$	3.14281	−	1.81450i	0.516674	−	0.298302i	−0.218899	−	0.975748i	$-0.570246\pi$
$37$	3.14281	−	1.81450i	0.516674	−	0.298302i	0.735573	+	0.677446i	$0.236913\pi$
$38$	1.67213			0.271255
$39$		0			0
$40$	0.145508			0.0230068
$41$	−1.12780	+	0.651136i	−0.176133	+	0.101690i	−0.585474	−	0.810691i	$-0.699092\pi$
$41$	−1.12780	+	0.651136i	−0.176133	+	0.101690i	0.409342	+	0.912381i	$0.365758\pi$
$42$		0			0
$43$	0.499222	−	0.864677i	0.0761306	−	0.131862i	−0.825447	−	0.564480i	$-0.809077\pi$
$43$	0.499222	−	0.864677i	0.0761306	−	0.131862i	0.901577	+	0.432618i	$0.142410\pi$
$44$			1.50961i			0.227582i
$45$		0			0
$46$	−4.76747	−	2.75250i	−0.702925	−	0.405834i
$47$			1.30183i			0.189891i	0.995482	+	0.0949455i	$0.0302677\pi$
$47$			1.30183i			0.189891i	−0.995482	+	0.0949455i	$0.969732\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−4.31179	+	2.48941i	−0.609779	+	0.352056i
$51$		0			0
$52$	−3.26575	+	1.52804i	−0.452878	+	0.211901i
$53$	5.12731			0.704290			0.352145	−	0.935945i	$-0.385452\pi$
$53$	5.12731			0.704290			0.352145	+	0.935945i	$0.385452\pi$
$54$		0			0
$55$	0.109830	+	0.190231i	0.0148095	+	0.0256507i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	−7.95821	−	4.59467i	−1.04496	−	0.603310i
$59$	2.78339	+	1.60699i	0.362367	+	0.209213i	0.670119	−	0.742254i	$-0.266243\pi$
$59$	2.78339	+	1.60699i	0.362367	+	0.209213i	−0.307751	+	0.951467i	$0.599577\pi$
$60$		0			0
$61$	1.63869	−	2.83829i	0.209813	−	0.363406i	−0.741843	−	0.670574i	$-0.766048\pi$
$61$	1.63869	−	2.83829i	0.209813	−	0.363406i	0.951655	+	0.307168i	$0.0993813\pi$
$62$	−0.439735	−	0.761644i	−0.0558464	−	0.0967289i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.300357	+	0.430148i	−0.0372546	+	0.0533533i
$66$		0			0
$67$	1.99785	−	1.15346i	0.244076	−	0.140917i	−0.372973	−	0.927842i	$-0.621661\pi$
$67$	1.99785	−	1.15346i	0.244076	−	0.140917i	0.617049	+	0.786925i	$0.288328\pi$
$68$	0.160487	+	0.277972i	0.0194619	+	0.0337090i
$69$		0			0
$70$		−	0.145508i		−	0.0173915i
$71$	6.10671	+	3.52571i	0.724733	+	0.418425i	0.816492	−	0.577356i	$-0.195916\pi$
$71$	6.10671	+	3.52571i	0.724733	+	0.418425i	−0.0917590	+	0.995781i	$0.529249\pi$
$72$		0			0
$73$			1.35714i			0.158841i	0.996841	+	0.0794205i	$0.0253070\pi$
$73$			1.35714i			0.158841i	−0.996841	+	0.0794205i	$0.974693\pi$
$74$	−1.81450	+	3.14281i	−0.210931	+	0.365344i
$75$		0			0
$76$	−1.44811	+	0.836065i	−0.166109	+	0.0959033i
$77$	1.50961			0.172036
$78$		0			0
$79$	8.66217			0.974570			0.487285	−	0.873243i	$-0.337987\pi$
$79$	8.66217			0.974570			0.487285	+	0.873243i	$0.337987\pi$
$80$	−0.126013	+	0.0727538i	−0.0140887	+	0.00813412i
$81$		0			0
$82$	0.651136	−	1.12780i	0.0719059	−	0.124545i
$83$			0.148560i			0.0163065i	0.999967	+	0.00815326i	$0.00259529\pi$
$83$			0.148560i			0.0163065i	−0.999967	+	0.00815326i	$0.997405\pi$
$84$		0			0
$85$	0.0404470	+	0.0233521i	0.00438709	+	0.00253289i
$86$			0.998443i			0.107665i
$87$		0			0
$88$	−0.754806	−	1.30736i	−0.0804626	−	0.139365i
$89$	7.13132	−	4.11727i	0.755918	−	0.436430i	−0.0719100	−	0.997411i	$-0.522909\pi$
$89$	7.13132	−	4.11727i	0.755918	−	0.436430i	0.827828	+	0.560981i	$0.189576\pi$
$90$		0			0
$91$	1.52804	+	3.26575i	0.160182	+	0.342343i
$92$	5.50500			0.573936
$93$		0			0
$94$	−0.650914	−	1.12742i	−0.0671366	−	0.116284i
$95$	−0.121654	+	0.210711i	−0.0124814	+	0.0216184i
$96$		0			0
$97$	11.4206	+	6.59366i	1.15958	+	0.669485i	0.951204	−	0.308564i	$-0.0998483\pi$
$97$	11.4206	+	6.59366i	1.15958	+	0.669485i	0.208378	+	0.978048i	$0.433182\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	2.48941	−	4.31179i	0.248941	−	0.431179i
$101$	7.66821	+	13.2817i	0.763015	+	1.32158i	0.941290	+	0.337600i	$0.109615\pi$
$101$	7.66821	+	13.2817i	0.763015	+	1.32158i	−0.178275	+	0.983981i	$0.557052\pi$
$102$		0			0
$103$	−2.10888			−0.207794			−0.103897	−	0.994588i	$-0.533131\pi$
$103$	−2.10888			−0.207794			−0.103897	+	0.994588i	$0.533131\pi$
$104$	2.06420	−	2.95619i	0.202411	−	0.289879i
$105$		0			0
$106$	−4.44038	+	2.56366i	−0.431288	+	0.249004i
$107$	−2.43608	−	4.21941i	−0.235505	−	0.407906i	0.723915	−	0.689890i	$-0.242341\pi$
$107$	−2.43608	−	4.21941i	−0.235505	−	0.407906i	−0.959419	+	0.281984i	$0.909008\pi$
$108$		0			0
$109$		−	10.4010i		−	0.996235i	−0.867110	−	0.498117i	$-0.834025\pi$
$109$		−	10.4010i		−	0.996235i	0.867110	−	0.498117i	$-0.165975\pi$
$110$	−0.190231	−	0.109830i	−0.0181378	−	0.0104719i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	−5.94751	+	10.3014i	−0.559495	+	0.969073i	0.438044	+	0.898954i	$0.355671\pi$
$113$	−5.94751	+	10.3014i	−0.559495	+	0.969073i	−0.997539	+	0.0701196i	$0.977662\pi$
$114$		0			0
$115$	0.693703	−	0.400510i	0.0646881	−	0.0373477i
$116$	9.18935			0.853209
$117$		0			0
$118$	−3.21399			−0.295872
$119$	0.277972	−	0.160487i	0.0254816	−	0.0147118i
$120$		0			0
$121$	−4.36054	+	7.55267i	−0.396412	+	0.686606i
$122$			3.27738i			0.296720i
$123$		0			0
$124$	0.761644	+	0.439735i	0.0683976	+	0.0394894i
$125$		−	1.45199i		−	0.129870i
$126$		0			0
$127$	3.08832	+	5.34913i	0.274044	+	0.474659i	0.969894	−	0.243529i	$-0.0783052\pi$
$127$	3.08832	+	5.34913i	0.274044	+	0.474659i	−0.695849	+	0.718188i	$0.744972\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	0.0450423	−	0.522698i	0.00395047	−	0.0458436i
$131$	−3.61986			−0.316269			−0.158134	−	0.987418i	$-0.550548\pi$
$131$	−3.61986			−0.316269			−0.158134	+	0.987418i	$0.550548\pi$
$132$		0			0
$133$	0.836065	+	1.44811i	0.0724961	+	0.125567i
$134$	−1.15346	+	1.99785i	−0.0996437	+	0.172588i
$135$		0			0
$136$	−0.277972	−	0.160487i	−0.0238359	−	0.0137617i
$137$	0.721249	+	0.416413i	0.0616205	+	0.0355766i	0.530494	−	0.847689i	$-0.322007\pi$
$137$	0.721249	+	0.416413i	0.0616205	+	0.0355766i	−0.468873	+	0.883265i	$0.655340\pi$
$138$		0			0
$139$	−10.2247	+	17.7098i	−0.867250	+	1.50212i	−0.00245526	+	0.999997i	$0.500782\pi$
$139$	−10.2247	+	17.7098i	−0.867250	+	1.50212i	−0.864795	+	0.502125i	$0.832552\pi$
$140$	0.0727538	+	0.126013i	0.00614881	+	0.0106501i
$141$		0			0
$142$	−7.05142			−0.591742
$143$	5.42288	+	0.467305i	0.453484	+	0.0390780i
$144$		0			0
$145$	1.15798	−	0.668559i	0.0961649	−	0.0555208i
$146$	−0.678569	−	1.17532i	−0.0561588	−	0.0972699i
$147$		0			0
$148$		−	3.62900i		−	0.298302i
$149$	−11.8482	−	6.84056i	−0.970642	−	0.560401i	−0.0712103	−	0.997461i	$-0.522686\pi$
$149$	−11.8482	−	6.84056i	−0.970642	−	0.560401i	−0.899432	+	0.437061i	$0.856019\pi$
$150$		0			0
$151$		−	0.670713i		−	0.0545819i	−0.999628	−	0.0272909i	$-0.991312\pi$
$151$		−	0.670713i		−	0.0545819i	0.999628	−	0.0272909i	$-0.00868806\pi$
$152$	0.836065	−	1.44811i	0.0678139	−	0.117457i
$153$		0			0
$154$	−1.30736	+	0.754806i	−0.105350	+	0.0608240i
$155$	0.127970			0.0102788
$156$		0			0
$157$	8.76914			0.699853			0.349927	−	0.936777i	$-0.386207\pi$
$157$	8.76914			0.699853			0.349927	+	0.936777i	$0.386207\pi$
$158$	−7.50166	+	4.33108i	−0.596800	+	0.344562i
$159$		0			0
$160$	0.0727538	−	0.126013i	0.00575169	−	0.00996222i
$161$		−	5.50500i		−	0.433855i
$162$		0			0
$163$	8.03647	+	4.63986i	0.629465	+	0.363422i	0.780545	−	0.625100i	$-0.214942\pi$
$163$	8.03647	+	4.63986i	0.629465	+	0.363422i	−0.151080	+	0.988522i	$0.548275\pi$
$164$			1.30227i			0.101690i
$165$		0			0
$166$	−0.0742798	−	0.128656i	−0.00576523	−	0.00998567i
$167$	−4.05876	+	2.34332i	−0.314076	+	0.181332i	−0.648749	−	0.761002i	$-0.724707\pi$
$167$	−4.05876	+	2.34332i	−0.314076	+	0.181332i	0.334673	+	0.942334i	$0.391374\pi$
$168$		0			0
$169$	4.47816	+	12.2043i	0.344474	+	0.938796i
$170$	−0.0467041			−0.00358204
$171$		0			0
$172$	−0.499222	−	0.864677i	−0.0380653	−	0.0659310i
$173$	9.43684	−	16.3451i	0.717470	−	1.24269i	−0.244530	−	0.969642i	$-0.578634\pi$
$173$	9.43684	−	16.3451i	0.717470	−	1.24269i	0.961999	−	0.273052i	$-0.0880331\pi$
$174$		0			0
$175$	−4.31179	−	2.48941i	−0.325941	−	0.188182i
$176$	1.30736	+	0.754806i	0.0985461	+	0.0568956i
$177$		0			0
$178$	−4.11727	+	7.13132i	−0.308602	+	0.534515i
$179$	8.97371	+	15.5429i	0.670727	+	1.16173i	0.977698	+	0.210014i	$0.0673510\pi$
$179$	8.97371	+	15.5429i	0.670727	+	1.16173i	−0.306972	+	0.951719i	$0.599316\pi$
$180$		0			0
$181$	10.0206			0.744825			0.372412	−	0.928067i	$-0.378531\pi$
$181$	10.0206			0.744825			0.372412	+	0.928067i	$0.378531\pi$
$182$	−2.95619	−	2.06420i	−0.219128	−	0.153009i
$183$		0			0
$184$	−4.76747	+	2.75250i	−0.351463	+	0.202917i
$185$	−0.264023	−	0.457302i	−0.0194114	−	0.0336215i
$186$		0			0
$187$		−	0.484546i		−	0.0354335i
$188$	1.12742	+	0.650914i	0.0822252	+	0.0474728i
$189$		0			0
$190$		−	0.243308i		−	0.0176514i
$191$	−3.82269	+	6.62109i	−0.276600	+	0.479085i	−0.970538	−	0.240950i	$-0.922541\pi$
$191$	−3.82269	+	6.62109i	−0.276600	+	0.479085i	0.693938	+	0.720035i	$0.255874\pi$
$192$		0			0
$193$	15.8631	−	9.15855i	1.14185	−	0.659247i	0.194961	−	0.980811i	$-0.437542\pi$
$193$	15.8631	−	9.15855i	1.14185	−	0.659247i	0.946888	+	0.321564i	$0.104209\pi$
$194$	−13.1873			−0.946794
$195$		0			0
$196$	1.00000			0.0714286
$197$	−13.9813	+	8.07212i	−0.996128	+	0.575115i	−0.907100	−	0.420915i	$-0.861709\pi$
$197$	−13.9813	+	8.07212i	−0.996128	+	0.575115i	−0.0890273	+	0.996029i	$0.528376\pi$
$198$		0			0
$199$	−12.9703	+	22.4652i	−0.919438	+	1.59251i	−0.119169	+	0.992874i	$0.538023\pi$
$199$	−12.9703	+	22.4652i	−0.919438	+	1.59251i	−0.800270	+	0.599640i	$0.795310\pi$
$200$			4.97883i			0.352056i
$201$		0			0
$202$	−13.2817	−	7.66821i	−0.934499	−	0.539533i
$203$		−	9.18935i		−	0.644966i
$204$		0			0
$205$	0.0947452	+	0.164103i	0.00661729	+	0.0114615i
$206$	1.82634	−	1.05444i	0.127247	−	0.0734662i
$207$		0			0
$208$	−0.309553	+	3.59224i	−0.0214636	+	0.249077i
$209$	2.52427			0.174607
$210$		0			0
$211$	5.02188	+	8.69815i	0.345721	+	0.598806i	0.985484	−	0.169766i	$-0.0543012\pi$
$211$	5.02188	+	8.69815i	0.345721	+	0.598806i	−0.639764	+	0.768572i	$0.720968\pi$
$212$	2.56366	−	4.44038i	0.176073	−	0.304967i
$213$		0			0
$214$	4.21941	+	2.43608i	0.288433	+	0.166527i
$215$	−0.125817	−	0.0726405i	−0.00858065	−	0.00495404i
$216$		0			0
$217$	0.439735	−	0.761644i	0.0298512	−	0.0517038i
$218$	5.20050	+	9.00753i	0.352222	+	0.610067i
$219$		0			0
$220$	0.219660			0.0148095
$221$	1.04822	−	0.490461i	0.0705109	−	0.0329920i
$222$		0			0
$223$	−7.39252	+	4.26807i	−0.495040	+	0.285811i	−0.726663	−	0.686994i	$-0.758930\pi$
$223$	−7.39252	+	4.26807i	−0.495040	+	0.285811i	0.231623	+	0.972806i	$0.425596\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$		−	11.8950i		−	0.791245i
$227$	−8.65098	−	4.99464i	−0.574186	−	0.331506i	0.184634	−	0.982807i	$-0.440890\pi$
$227$	−8.65098	−	4.99464i	−0.574186	−	0.331506i	−0.758819	+	0.651301i	$0.774223\pi$
$228$		0			0
$229$		−	18.1455i		−	1.19909i	−0.800341	−	0.599544i	$-0.795348\pi$
$229$		−	18.1455i		−	1.19909i	0.800341	−	0.599544i	$-0.204652\pi$
$230$	−0.400510	+	0.693703i	−0.0264088	+	0.0457414i
$231$		0			0
$232$	−7.95821	+	4.59467i	−0.522482	+	0.301655i
$233$	3.58850			0.235091			0.117545	−	0.993068i	$-0.462497\pi$
$233$	3.58850			0.235091			0.117545	+	0.993068i	$0.462497\pi$
$234$		0			0
$235$	0.189426			0.0123568
$236$	2.78339	−	1.60699i	0.181184	−	0.104606i
$237$		0			0
$238$	−0.160487	+	0.277972i	−0.0104028	+	0.0180182i
$239$			12.0553i			0.779794i	0.920858	+	0.389897i	$0.127489\pi$
$239$			12.0553i			0.779794i	−0.920858	+	0.389897i	$0.872511\pi$
$240$		0			0
$241$	9.68612	+	5.59229i	0.623938	+	0.360231i	0.778401	−	0.627768i	$-0.216031\pi$
$241$	9.68612	+	5.59229i	0.623938	+	0.360231i	−0.154463	+	0.987999i	$0.549365\pi$
$242$		−	8.72107i		−	0.560612i
$243$		0			0
$244$	−1.63869	−	2.83829i	−0.104906	−	0.181703i
$245$	0.126013	−	0.0727538i	0.00805069	−	0.00464807i
$246$		0			0
$247$	2.55508	+	5.46076i	0.162576	+	0.347460i
$248$	−0.879471			−0.0558464
$249$		0			0
$250$	0.725997	+	1.25746i	0.0459161	+	0.0795290i
$251$	8.28386	−	14.3481i	0.522873	−	0.905642i	−0.476773	−	0.879027i	$-0.658194\pi$
$251$	8.28386	−	14.3481i	0.522873	−	0.905642i	0.999646	−	0.0266158i	$-0.00847308\pi$
$252$		0			0
$253$	−7.19703	−	4.15521i	−0.452473	−	0.261236i
$254$	−5.34913	−	3.08832i	−0.335634	−	0.193779i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.63157	−	16.6824i	−0.600801	−	1.04062i	−0.992700	−	0.120610i	$-0.961515\pi$
$257$	−9.63157	−	16.6824i	−0.600801	−	1.04062i	0.391899	−	0.920008i	$-0.371818\pi$
$258$		0			0
$259$	−3.62900			−0.225495
$260$	0.222341	+	0.475191i	0.0137890	+	0.0294701i
$261$		0			0
$262$	3.13489	−	1.80993i	0.193674	−	0.111818i
$263$	−8.66445	−	15.0073i	−0.534273	−	0.925388i	−0.999198	−	0.0400377i	$-0.987252\pi$
$263$	−8.66445	−	15.0073i	−0.534273	−	0.925388i	0.464925	−	0.885350i	$-0.346081\pi$
$264$		0			0
$265$		−	0.746062i		−	0.0458302i
$266$	−1.44811	−	0.836065i	−0.0887892	−	0.0512625i
$267$		0			0
$268$		−	2.30692i		−	0.140917i
$269$	−5.13383	+	8.89206i	−0.313015	+	0.542158i	−0.979014	−	0.203795i	$-0.934672\pi$
$269$	−5.13383	+	8.89206i	−0.313015	+	0.542158i	0.665998	+	0.745953i	$0.268006\pi$
$270$		0			0
$271$	1.46333	−	0.844854i	0.0888909	−	0.0513212i	−0.454896	−	0.890545i	$-0.650323\pi$
$271$	1.46333	−	0.844854i	0.0888909	−	0.0513212i	0.543787	+	0.839224i	$0.316990\pi$
$272$	0.320974			0.0194619
$273$		0			0
$274$	−0.832827			−0.0503129
$275$	−6.50913	+	3.75805i	−0.392515	+	0.226619i
$276$		0			0
$277$	7.28198	−	12.6128i	0.437532	−	0.757827i	−0.559967	−	0.828515i	$-0.689186\pi$
$277$	7.28198	−	12.6128i	0.437532	−	0.757827i	0.997498	+	0.0706879i	$0.0225195\pi$
$278$		−	20.4495i		−	1.22648i
$279$		0			0
$280$	−0.126013	−	0.0727538i	−0.00753073	−	0.00434787i
$281$			21.9861i			1.31158i	0.754943	+	0.655790i	$0.227664\pi$
$281$			21.9861i			1.31158i	−0.754943	+	0.655790i	$0.772336\pi$
$282$		0			0
$283$	−10.5460	−	18.2662i	−0.626893	−	1.08581i	−0.988171	−	0.153353i	$-0.950993\pi$
$283$	−10.5460	−	18.2662i	−0.626893	−	1.08581i	0.361278	−	0.932458i	$-0.382341\pi$
$284$	6.10671	−	3.52571i	0.362367	−	0.209212i
$285$		0			0
$286$	−4.93001	+	2.30674i	−0.291517	+	0.136401i
$287$	1.30227			0.0768707
$288$		0			0
$289$	8.44849	+	14.6332i	0.496970	+	0.860777i
$290$	−0.668559	+	1.15798i	−0.0392592	+	0.0679989i
$291$		0			0
$292$	1.17532	+	0.678569i	0.0687802	+	0.0397103i
$293$	−11.3293	−	6.54097i	−0.661864	−	0.382128i	0.131123	−	0.991366i	$-0.458142\pi$
$293$	−11.3293	−	6.54097i	−0.661864	−	0.382128i	−0.792987	+	0.609239i	$0.791475\pi$
$294$		0			0
$295$	0.233830	−	0.405005i	0.0136141	−	0.0235803i
$296$	1.81450	+	3.14281i	0.105466	+	0.182672i
$297$		0			0
$298$	13.6811			0.792526
$299$	1.70409	−	19.7753i	0.0985501	−	1.14363i
$300$		0			0
$301$	−0.864677	+	0.499222i	−0.0498392	+	0.0287747i
$302$	0.335357	+	0.580855i	0.0192976	+	0.0334244i
$303$		0			0
$304$			1.67213i			0.0959033i
$305$	−0.412993	−	0.238441i	−0.0236479	−	0.0136531i
$306$		0			0
$307$			27.5551i			1.57266i	0.617810	+	0.786328i	$0.288020\pi$
$307$			27.5551i			1.57266i	−0.617810	+	0.786328i	$0.711980\pi$
$308$	0.754806	−	1.30736i	0.0430090	−	0.0744939i
$309$		0			0
$310$	−0.110825	+	0.0639848i	−0.00629443	+	0.00363409i
$311$	9.19192			0.521226			0.260613	−	0.965443i	$-0.416075\pi$
$311$	9.19192			0.521226			0.260613	+	0.965443i	$0.416075\pi$
$312$		0			0
$313$	25.4372			1.43779			0.718897	−	0.695117i	$-0.244647\pi$
$313$	25.4372			1.43779			0.718897	+	0.695117i	$0.244647\pi$
$314$	−7.59429	+	4.38457i	−0.428571	+	0.247435i
$315$		0			0
$316$	4.33108	−	7.50166i	0.243642	−	0.422001i
$317$		−	26.0786i		−	1.46472i	−0.680917	−	0.732361i	$-0.738418\pi$
$317$		−	26.0786i		−	1.46472i	0.680917	−	0.732361i	$-0.261582\pi$
$318$		0			0
$319$	−12.0138	−	6.93617i	−0.672644	−	0.388351i
$320$			0.145508i			0.00813412i
$321$		0			0
$322$	2.75250	+	4.76747i	0.153391	+	0.265681i
$323$	0.464805	−	0.268355i	0.0258624	−	0.0149317i
$324$		0			0
$325$	−14.7184	−	10.2773i	−0.816429	−	0.570082i
$326$	−9.27972			−0.513956
$327$		0			0
$328$	−0.651136	−	1.12780i	−0.0359530	−	0.0622724i
$329$	0.650914	−	1.12742i	0.0358860	−	0.0621564i
$330$		0			0
$331$	−3.80635	−	2.19759i	−0.209216	−	0.120791i	0.391731	−	0.920080i	$-0.371876\pi$
$331$	−3.80635	−	2.19759i	−0.209216	−	0.120791i	−0.600947	+	0.799289i	$0.705210\pi$
$332$	0.128656	+	0.0742798i	0.00706093	+	0.00407663i
$333$		0			0
$334$	2.34332	−	4.05876i	0.128221	−	0.222085i
$335$	−0.167837	−	0.290702i	−0.00916991	−	0.0158828i
$336$		0			0
$337$	−9.08845			−0.495080			−0.247540	−	0.968878i	$-0.579622\pi$
$337$	−9.08845			−0.495080			−0.247540	+	0.968878i	$0.579622\pi$
$338$	−9.98037	−	8.33020i	−0.542861	−	0.453103i
$339$		0			0
$340$	0.0404470	−	0.0233521i	0.00219355	−	0.00126644i
$341$	−0.663829	−	1.14979i	−0.0359484	−	0.0622644i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	0.864677	+	0.499222i	0.0466203	+	0.0269162i
$345$		0			0
$346$			18.8737i			1.01466i
$347$	−6.90968	+	11.9679i	−0.370931	+	0.642471i	−0.989709	−	0.143095i	$-0.954295\pi$
$347$	−6.90968	+	11.9679i	−0.370931	+	0.642471i	0.618778	+	0.785566i	$0.287628\pi$
$348$		0			0
$349$	20.2260	−	11.6775i	1.08267	−	0.625082i	0.151057	−	0.988525i	$-0.451732\pi$
$349$	20.2260	−	11.6775i	1.08267	−	0.625082i	0.931616	+	0.363443i	$0.118399\pi$
$350$	4.97883			0.266130
$351$		0			0
$352$	−1.50961			−0.0804626
$353$	−16.9040	+	9.75955i	−0.899711	+	0.519448i	−0.877106	−	0.480296i	$-0.840529\pi$
$353$	−16.9040	+	9.75955i	−0.899711	+	0.519448i	−0.0226046	+	0.999744i	$0.507196\pi$
$354$		0			0
$355$	0.513017	−	0.888572i	0.0272281	−	0.0471605i
$356$		−	8.23454i		−	0.436430i
$357$		0			0
$358$	−15.5429	−	8.97371i	−0.821469	−	0.474275i
$359$		−	31.0158i		−	1.63695i	−0.574542	−	0.818475i	$-0.694820\pi$
$359$		−	31.0158i		−	1.63695i	0.574542	−	0.818475i	$-0.305180\pi$
$360$		0			0
$361$	−8.10199	−	14.0331i	−0.426420	−	0.738582i
$362$	−8.67809	+	5.01030i	−0.456110	+	0.263335i
$363$		0			0
$364$	3.59224	+	0.309553i	0.188284	+	0.0162250i
$365$	0.197474			0.0103363
$366$		0			0
$367$	0.155016	+	0.268496i	0.00809178	+	0.0140154i	0.870043	−	0.492976i	$-0.164091\pi$
$367$	0.155016	+	0.268496i	0.00809178	+	0.0140154i	−0.861951	+	0.506991i	$0.830758\pi$
$368$	2.75250	−	4.76747i	0.143484	−	0.248522i
$369$		0			0
$370$	0.457302	+	0.264023i	0.0237740	+	0.0137259i
$371$	−4.44038	−	2.56366i	−0.230533	−	0.133098i
$372$		0			0
$373$	4.99428	−	8.65035i	0.258594	−	0.447898i	−0.707271	−	0.706942i	$-0.750074\pi$
$373$	4.99428	−	8.65035i	0.258594	−	0.447898i	0.965866	+	0.259044i	$0.0834075\pi$
$374$	0.242273	+	0.419629i	0.0125276	+	0.0216985i
$375$		0			0
$376$	−1.30183			−0.0671366
$377$	2.84459	−	33.0103i	0.146504	−	1.70012i
$378$		0			0
$379$	−11.3451	+	6.55010i	−0.582759	+	0.336456i	−0.762229	−	0.647308i	$-0.775895\pi$
$379$	−11.3451	+	6.55010i	−0.582759	+	0.336456i	0.179470	+	0.983763i	$0.442562\pi$
$380$	0.121654	+	0.210711i	0.00624071	+	0.0108092i
$381$		0			0
$382$		−	7.64537i		−	0.391171i
$383$	−26.9468	−	15.5577i	−1.37692	−	0.794962i	−0.385128	−	0.922863i	$-0.625843\pi$
$383$	−26.9468	−	15.5577i	−1.37692	−	0.794962i	−0.991787	+	0.127901i	$0.959176\pi$
$384$		0			0
$385$		−	0.219660i		−	0.0111949i
$386$	−9.15855	+	15.8631i	−0.466158	+	0.807409i
$387$		0			0
$388$	11.4206	−	6.59366i	0.579791	−	0.334742i
$389$	−8.82237			−0.447312			−0.223656	−	0.974668i	$-0.571799\pi$
$389$	−8.82237			−0.447312			−0.223656	+	0.974668i	$0.571799\pi$
$390$		0			0
$391$	−1.76696			−0.0893592
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	8.07212	−	13.9813i	0.406667	−	0.704369i
$395$		−	1.26041i		−	0.0634181i
$396$		0			0
$397$	7.41327	+	4.28006i	0.372062	+	0.214810i	0.674359	−	0.738404i	$-0.264420\pi$
$397$	7.41327	+	4.28006i	0.372062	+	0.214810i	−0.302297	+	0.953214i	$0.597753\pi$
$398$		−	25.9406i		−	1.30028i
$399$		0			0
$400$	−2.48941	−	4.31179i	−0.124471	−	0.215590i
$401$	3.80943	−	2.19937i	0.190234	−	0.109831i	−0.401858	−	0.915702i	$-0.631636\pi$
$401$	3.80943	−	2.19937i	0.190234	−	0.109831i	0.592092	+	0.805870i	$0.298302\pi$
$402$		0			0
$403$	1.81540	−	2.59989i	0.0904317	−	0.129510i
$404$	15.3364			0.763015
$405$		0			0
$406$	4.59467	+	7.95821i	0.228030	+	0.394959i
$407$	−2.73919	+	4.74442i	−0.135777	+	0.235172i
$408$		0			0
$409$	−14.3012	−	8.25679i	−0.707148	−	0.408272i	0.102856	−	0.994696i	$-0.467202\pi$
$409$	−14.3012	−	8.25679i	−0.707148	−	0.408272i	−0.810004	+	0.586424i	$0.800535\pi$
$410$	−0.164103	−	0.0947452i	−0.00810449	−	0.00467913i
$411$		0			0
$412$	−1.05444	+	1.82634i	−0.0519484	+	0.0899773i
$413$	−1.60699	−	2.78339i	−0.0790750	−	0.136962i
$414$		0			0
$415$	0.0216165			0.00106111
$416$	−1.52804	−	3.26575i	−0.0749182	−	0.160116i
$417$		0			0
$418$	−2.18608	+	1.26213i	−0.106925	+	0.0617330i
$419$	−16.4980	−	28.5753i	−0.805979	−	1.39600i	−0.915628	−	0.402027i	$-0.868306\pi$
$419$	−16.4980	−	28.5753i	−0.805979	−	1.39600i	0.109649	−	0.993970i	$-0.465027\pi$
$420$		0			0
$421$			1.67311i			0.0815425i	0.999169	+	0.0407713i	$0.0129815\pi$
$421$			1.67311i			0.0815425i	−0.999169	+	0.0407713i	$0.987019\pi$
$422$	−8.69815	−	5.02188i	−0.423419	−	0.244461i
$423$		0			0
$424$			5.12731i			0.249004i
$425$	−0.799037	+	1.38397i	−0.0387590	+	0.0671326i
$426$		0			0
$427$	−2.83829	+	1.63869i	−0.137355	+	0.0793017i
$428$	−4.87216			−0.235505
$429$		0			0
$430$	0.145281			0.00700607
$431$	−5.64693	+	3.26026i	−0.272003	+	0.157041i	−0.629798	−	0.776759i	$-0.716862\pi$
$431$	−5.64693	+	3.26026i	−0.272003	+	0.157041i	0.357794	+	0.933800i	$0.383529\pi$
$432$		0			0
$433$	−0.0128517	+	0.0222598i	−0.000617613	+	0.00106974i	−0.866334	−	0.499465i	$-0.833530\pi$
$433$	−0.0128517	+	0.0222598i	−0.000617613	+	0.00106974i	0.865716	+	0.500535i	$0.166863\pi$
$434$			0.879471i			0.0422159i
$435$		0			0
$436$	−9.00753	−	5.20050i	−0.431382	−	0.249059i
$437$		−	9.20508i		−	0.440339i
$438$		0			0
$439$	−15.0983	−	26.1509i	−0.720600	−	1.24812i	−0.960760	−	0.277383i	$-0.910533\pi$
$439$	−15.0983	−	26.1509i	−0.720600	−	1.24812i	0.240159	−	0.970733i	$-0.422800\pi$
$440$	−0.190231	+	0.109830i	−0.00906890	+	0.00523593i
$441$		0			0
$442$	−0.662555	+	0.948861i	−0.0315145	+	0.0451327i
$443$	21.4059			1.01703			0.508513	−	0.861054i	$-0.330195\pi$
$443$	21.4059			1.01703			0.508513	+	0.861054i	$0.330195\pi$
$444$		0			0
$445$	−0.599094	−	1.03766i	−0.0283998	−	0.0491898i
$446$	4.26807	−	7.39252i	0.202099	−	0.350046i
$447$		0			0
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	26.3724	+	15.2261i	1.24459	+	0.718565i	0.970026	−	0.243003i	$-0.0781325\pi$
$449$	26.3724	+	15.2261i	1.24459	+	0.718565i	0.274566	+	0.961568i	$0.411466\pi$
$450$		0			0
$451$	0.982962	−	1.70254i	0.0462859	−	0.0801695i
$452$	5.94751	+	10.3014i	0.279747	+	0.484537i
$453$		0			0
$454$	9.98929			0.468821
$455$	0.475191	−	0.222341i	0.0222773	−	0.0104235i
$456$		0			0
$457$	10.9024	−	6.29450i	0.509992	−	0.294444i	−0.222838	−	0.974855i	$-0.571532\pi$
$457$	10.9024	−	6.29450i	0.509992	−	0.294444i	0.732830	+	0.680411i	$0.238199\pi$
$458$	9.07275	+	15.7145i	0.423942	+	0.734289i
$459$		0			0
$460$		−	0.801019i		−	0.0373477i
$461$	−9.54400	−	5.51023i	−0.444509	−	0.256637i	0.261000	−	0.965339i	$-0.415948\pi$
$461$	−9.54400	−	5.51023i	−0.444509	−	0.256637i	−0.705508	+	0.708702i	$0.749281\pi$
$462$		0			0
$463$		−	1.37834i		−	0.0640569i	−0.999487	−	0.0320285i	$-0.989803\pi$
$463$		−	1.37834i		−	0.0640569i	0.999487	−	0.0320285i	$-0.0101967\pi$
$464$	4.59467	−	7.95821i	0.213302	−	0.369450i
$465$		0			0
$466$	−3.10774	+	1.79425i	−0.143963	+	0.0831171i
$467$	18.2967			0.846672			0.423336	−	0.905973i	$-0.360859\pi$
$467$	18.2967			0.846672			0.423336	+	0.905973i	$0.360859\pi$
$468$		0			0
$469$	−2.30692			−0.106524
$470$	−0.164047	+	0.0947128i	−0.00756694	+	0.00436878i
$471$		0			0
$472$	−1.60699	+	2.78339i	−0.0739679	+	0.128116i
$473$			1.50726i			0.0693039i
$474$		0			0
$475$	−7.20988	−	4.16263i	−0.330812	−	0.190994i
$476$		−	0.320974i		−	0.0147118i
$477$		0			0
$478$	−6.02766	−	10.4402i	−0.275699	−	0.477524i
$479$	−23.5123	+	13.5748i	−1.07430	+	0.620249i	−0.929354	−	0.369190i	$-0.879635\pi$
$479$	−23.5123	+	13.5748i	−1.07430	+	0.620249i	−0.144949	+	0.989439i	$0.546302\pi$
$480$		0			0
$481$	−13.0362	−	1.12337i	−0.594401	−	0.0512212i
$482$	−11.1846			−0.509443
$483$		0			0
$484$	4.36054	+	7.55267i	0.198206	+	0.343303i
$485$	0.959427	−	1.66178i	0.0435653	−	0.0754574i
$486$		0			0
$487$	−18.0511	−	10.4218i	−0.817973	−	0.472257i	0.0317439	−	0.999496i	$-0.489894\pi$
$487$	−18.0511	−	10.4218i	−0.817973	−	0.472257i	−0.849717	+	0.527239i	$0.823227\pi$
$488$	2.83829	+	1.63869i	0.128483	+	0.0741799i
$489$		0			0
$490$	−0.0727538	+	0.126013i	−0.00328668	+	0.00569270i
$491$	12.3228	+	21.3438i	0.556122	+	0.963232i	0.997815	+	0.0660655i	$0.0210446\pi$
$491$	12.3228	+	21.3438i	0.556122	+	0.963232i	−0.441693	+	0.897166i	$0.645622\pi$
$492$		0			0
$493$	−2.94954			−0.132841
$494$	−4.94314	−	3.45161i	−0.222402	−	0.155295i
$495$		0			0
$496$	0.761644	−	0.439735i	0.0341988	−	0.0197447i
$497$	−3.52571	−	6.10671i	−0.158150	−	0.273923i
$498$		0			0
$499$		−	1.04444i		−	0.0467556i	−0.999727	−	0.0233778i	$-0.992558\pi$
$499$		−	1.04444i		−	0.0467556i	0.999727	−	0.0233778i	$-0.00744206\pi$
$500$	−1.25746	−	0.725997i	−0.0562355	−	0.0324676i
$501$		0			0
$502$			16.5677i			0.739454i
$503$	10.2839	−	17.8123i	0.458538	−	0.794212i	−0.540346	−	0.841443i	$-0.681706\pi$
$503$	10.2839	−	17.8123i	0.458538	−	0.794212i	0.998884	+	0.0472314i	$0.0150398\pi$
$504$		0			0
$505$	1.93259	−	1.11578i	0.0859991	−	0.0496516i
$506$	8.31041			0.369443
$507$		0			0
$508$	6.17664			0.274044
$509$	−29.5532	+	17.0625i	−1.30992	+	0.756283i	−0.982083	−	0.188451i	$-0.939653\pi$
$509$	−29.5532	+	17.0625i	−1.30992	+	0.756283i	−0.327838	+	0.944734i	$0.606320\pi$
$510$		0			0
$511$	0.678569	−	1.17532i	0.0300181	−	0.0519929i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	16.6824	+	9.63157i	0.735828	+	0.424830i
$515$			0.306857i			0.0135217i
$516$		0			0
$517$	−0.982627	−	1.70196i	−0.0432159	−	0.0748521i
$518$	3.14281	−	1.81450i	0.138087	−	0.0797246i
$519$		0			0
$520$	−0.430148	−	0.300357i	−0.0188633	−	0.0131715i
$521$	26.5476			1.16307			0.581535	−	0.813521i	$-0.302452\pi$
$521$	26.5476			1.16307			0.581535	+	0.813521i	$0.302452\pi$
$522$		0			0
$523$	−7.25999	−	12.5747i	−0.317457	−	0.549852i	0.662500	−	0.749062i	$-0.269496\pi$
$523$	−7.25999	−	12.5747i	−0.317457	−	0.549852i	−0.979957	+	0.199210i	$0.936162\pi$
$524$	−1.80993	+	3.13489i	−0.0790672	+	0.136948i
$525$		0			0
$526$	15.0073	+	8.66445i	0.654348	+	0.377788i
$527$	−0.244468	−	0.141144i	−0.0106492	−	0.00614831i
$528$		0			0
$529$	−3.65253	+	6.32636i	−0.158806	+	0.275059i
$530$	0.373031	+	0.646109i	0.0162034	+	0.0280652i
$531$		0			0
$532$	1.67213			0.0724961
$533$	4.67807	+	0.403122i	0.202630	+	0.0174612i
$534$		0			0
$535$	−0.613956	+	0.354468i	−0.0265436	+	0.0153250i
$536$	1.15346	+	1.99785i	0.0498219	+	0.0862940i
$537$		0			0
$538$		−	10.2677i		−	0.442670i
$539$	−1.30736	−	0.754806i	−0.0563121	−	0.0325118i
$540$		0			0
$541$			4.87496i			0.209591i	0.994494	+	0.104795i	$0.0334188\pi$
$541$			4.87496i			0.209591i	−0.994494	+	0.104795i	$0.966581\pi$
$542$	−0.844854	+	1.46333i	−0.0362896	+	0.0628554i
$543$		0			0
$544$	−0.277972	+	0.160487i	−0.0119179	+	0.00688083i
$545$	−1.51342			−0.0648279
$546$		0			0
$547$	33.4435			1.42994			0.714970	−	0.699155i	$-0.246440\pi$
$547$	33.4435			1.42994			0.714970	+	0.699155i	$0.246440\pi$
$548$	0.721249	−	0.416413i	0.0308102	−	0.0177883i
$549$		0			0
$550$	3.75805	−	6.50913i	0.160244	−	0.277550i
$551$		−	15.3658i		−	0.654605i
$552$		0			0
$553$	−7.50166	−	4.33108i	−0.319003	−	0.184176i
$554$			14.5640i			0.618763i
$555$		0			0
$556$	10.2247	+	17.7098i	0.433625	+	0.751061i
$557$	0.462539	−	0.267047i	0.0195984	−	0.0113151i	−0.490169	−	0.871628i	$-0.663065\pi$
$557$	0.462539	−	0.267047i	0.0195984	−	0.0113151i	0.509767	+	0.860312i	$0.329732\pi$
$558$		0			0
$559$	−3.26066	+	1.52566i	−0.137911	+	0.0645285i
$560$	0.145508			0.00614881
$561$		0			0
$562$	−10.9930	−	19.0405i	−0.463714	−	0.803176i
$563$	−11.4298	+	19.7970i	−0.481708	+	0.834343i	−0.999780	−	0.0209944i	$-0.993317\pi$
$563$	−11.4298	+	19.7970i	−0.481708	+	0.834343i	0.518072	+	0.855337i	$0.326650\pi$
$564$		0			0
$565$	1.49893	+	0.865407i	0.0630604	+	0.0364080i
$566$	18.2662	+	10.5460i	0.767784	+	0.443281i
$567$		0			0
$568$	−3.52571	+	6.10671i	−0.147936	+	0.256232i
$569$	2.23622	+	3.87326i	0.0937474	+	0.162375i	0.909085	−	0.416610i	$-0.136782\pi$
$569$	2.23622	+	3.87326i	0.0937474	+	0.162375i	−0.815338	+	0.578986i	$0.803449\pi$
$570$		0			0
$571$	−10.3978			−0.435135			−0.217568	−	0.976045i	$-0.569812\pi$
$571$	−10.3978			−0.435135			−0.217568	+	0.976045i	$0.569812\pi$
$572$	3.11614	−	4.46270i	0.130292	−	0.186595i
$573$		0			0
$574$	−1.12780	+	0.651136i	−0.0470735	+	0.0271779i
$575$	13.7042	+	23.7364i	0.571506	+	0.989877i
$576$		0			0
$577$		−	16.4498i		−	0.684814i	−0.939552	−	0.342407i	$-0.888758\pi$
$577$		−	16.4498i		−	0.684814i	0.939552	−	0.342407i	$-0.111242\pi$
$578$	−14.6332	−	8.44849i	−0.608661	−	0.351411i
$579$		0			0
$580$		−	1.33712i		−	0.0555208i
$581$	0.0742798	−	0.128656i	0.00308164	−	0.00533756i
$582$		0			0
$583$	−6.70325	+	3.87012i	−0.277620	+	0.160284i
$584$	−1.35714			−0.0561588
$585$		0			0
$586$	13.0819			0.540410
$587$	−2.63207	+	1.51963i	−0.108637	+	0.0627218i	−0.553334	−	0.832959i	$-0.686645\pi$
$587$	−2.63207	+	1.51963i	−0.108637	+	0.0627218i	0.444697	+	0.895681i	$0.353311\pi$
$588$		0			0
$589$	0.735295	−	1.27357i	0.0302973	−	0.0524765i
$590$			0.467659i			0.0192532i
$591$		0			0
$592$	−3.14281	−	1.81450i	−0.129169	−	0.0745755i
$593$		−	14.4226i		−	0.592266i	−0.955147	−	0.296133i	$-0.904303\pi$
$593$		−	14.4226i		−	0.592266i	0.955147	−	0.296133i	$-0.0956972\pi$
$594$		0			0
$595$	−0.0233521	−	0.0404470i	−0.000957342	−	0.00165816i
$596$	−11.8482	+	6.84056i	−0.485321	+	0.280200i
$597$		0			0
$598$	8.41186	+	17.9779i	0.343986	+	0.735173i
$599$	−9.47450			−0.387118			−0.193559	−	0.981089i	$-0.562003\pi$
$599$	−9.47450			−0.387118			−0.193559	+	0.981089i	$0.562003\pi$
$600$		0			0
$601$	10.7733	+	18.6600i	0.439453	+	0.761156i	0.997647	−	0.0685550i	$-0.0218388\pi$
$601$	10.7733	+	18.6600i	0.439453	+	0.761156i	−0.558194	+	0.829710i	$0.688506\pi$
$602$	0.499222	−	0.864677i	0.0203468	−	0.0352416i
$603$		0			0
$604$	−0.580855	−	0.335357i	−0.0236347	−	0.0136455i
$605$	1.09897	+	0.634491i	0.0446795	+	0.0257957i
$606$		0			0
$607$	−11.5724	+	20.0439i	−0.469708	+	0.813558i	−0.999400	−	0.0346319i	$-0.988974\pi$
$607$	−11.5724	+	20.0439i	−0.469708	+	0.813558i	0.529692	+	0.848190i	$0.322307\pi$
$608$	−0.836065	−	1.44811i	−0.0339069	−	0.0587285i
$609$		0			0
$610$	0.476883			0.0193084
$611$	2.68723	−	3.84845i	0.108714	−	0.155692i
$612$		0			0
$613$	9.72308	−	5.61362i	0.392711	−	0.226732i	−0.290623	−	0.956838i	$-0.593862\pi$
$613$	9.72308	−	5.61362i	0.392711	−	0.226732i	0.683334	+	0.730106i	$0.260529\pi$
$614$	−13.7776	−	23.8635i	−0.556018	−	0.963051i
$615$		0			0
$616$			1.50961i			0.0608240i
$617$	−14.8368	−	8.56601i	−0.597305	−	0.344854i	0.170675	−	0.985327i	$-0.445405\pi$
$617$	−14.8368	−	8.56601i	−0.597305	−	0.344854i	−0.767981	+	0.640473i	$0.778738\pi$
$618$		0			0
$619$		−	4.05509i		−	0.162988i	−0.996674	−	0.0814938i	$-0.974031\pi$
$619$		−	4.05509i		−	0.162988i	0.996674	−	0.0814938i	$-0.0259691\pi$
$620$	0.0639848	−	0.110825i	0.00256969	−	0.00445084i
$621$		0			0
$622$	−7.96044	+	4.59596i	−0.319185	+	0.184281i
$623$	−8.23454			−0.329910
$624$		0			0
$625$	24.6829			0.987314
$626$	−22.0292	+	12.7186i	−0.880465	+	0.508337i
$627$		0			0
$628$	4.38457	−	7.59429i	0.174963	−	0.303045i
$629$			1.16482i			0.0464442i
$630$		0			0
$631$	−3.27784	−	1.89246i	−0.130489	−	0.0753378i	0.433335	−	0.901233i	$-0.357337\pi$
$631$	−3.27784	−	1.89246i	−0.130489	−	0.0753378i	−0.563823	+	0.825895i	$0.690670\pi$
$632$			8.66217i			0.344562i
$633$		0			0
$634$	13.0393	+	22.5848i	0.517857	+	0.896955i
$635$	0.778339	−	0.449374i	0.0308874	−	0.0178329i
$636$		0			0
$637$	0.309553	−	3.59224i	0.0122649	−	0.142330i
$638$	13.8723			0.549211
$639$		0			0
$640$	−0.0727538	−	0.126013i	−0.00287584	−	0.00498111i
$641$	−4.17476	+	7.23090i	−0.164893	+	0.285604i	−0.936617	−	0.350354i	$-0.886061\pi$
$641$	−4.17476	+	7.23090i	−0.164893	+	0.285604i	0.771724	+	0.635957i	$0.219395\pi$
$642$		0			0
$643$	−27.2735	−	15.7464i	−1.07556	−	0.620976i	−0.145866	−	0.989304i	$-0.546597\pi$
$643$	−27.2735	−	15.7464i	−1.07556	−	0.620976i	−0.929696	+	0.368328i	$0.879930\pi$
$644$	−4.76747	−	2.75250i	−0.187865	−	0.108464i
$645$		0			0
$646$	−0.268355	+	0.464805i	−0.0105583	+	0.0182875i
$647$	21.3575	+	36.9922i	0.839649	+	1.45432i	0.890188	+	0.455593i	$0.150573\pi$
$647$	21.3575	+	36.9922i	0.839649	+	1.45432i	−0.0505387	+	0.998722i	$0.516094\pi$
$648$		0			0
$649$	−4.85187			−0.190453
$650$	17.8851	+	1.54121i	0.701513	+	0.0604513i
$651$		0			0
$652$	8.03647	−	4.63986i	0.314732	−	0.181711i
$653$	−4.55714	−	7.89321i	−0.178335	−	0.308885i	0.762975	−	0.646427i	$-0.223738\pi$
$653$	−4.55714	−	7.89321i	−0.178335	−	0.308885i	−0.941310	+	0.337542i	$0.890404\pi$
$654$		0			0
$655$			0.526717i			0.0205805i
$656$	1.12780	+	0.651136i	0.0440332	+	0.0254226i
$657$		0			0
$658$			1.30183i			0.0507505i
$659$	−23.9967	+	41.5635i	−0.934778	+	1.61908i	−0.159748	+	0.987158i	$0.551068\pi$
$659$	−23.9967	+	41.5635i	−0.934778	+	1.61908i	−0.775030	+	0.631924i	$0.782265\pi$
$660$		0			0
$661$	−12.1581	+	7.01949i	−0.472896	+	0.273026i	−0.717451	−	0.696609i	$-0.754691\pi$
$661$	−12.1581	+	7.01949i	−0.472896	+	0.273026i	0.244556	+	0.969635i	$0.421358\pi$
$662$	4.39519			0.170824
$663$		0			0
$664$	−0.148560			−0.00576523
$665$	0.210711	−	0.121654i	0.00817100	−	0.00471753i
$666$		0			0
$667$	−25.2937	+	43.8099i	−0.979375	+	1.69633i
$668$			4.68665i			0.181332i
$669$		0			0
$670$	0.290702	+	0.167837i	0.0112308	+	0.00648411i
$671$			4.94757i			0.190999i
$672$		0			0
$673$	−4.01666	−	6.95706i	−0.154831	−	0.268175i	0.778167	−	0.628058i	$-0.216150\pi$
$673$	−4.01666	−	6.95706i	−0.154831	−	0.268175i	−0.932997	+	0.359883i	$0.882817\pi$
$674$	7.87083	−	4.54423i	0.303173	−	0.175037i
$675$		0			0
$676$	12.8084	+	2.22398i	0.492629	+	0.0855376i
$677$	5.93746			0.228195			0.114098	−	0.993470i	$-0.463602\pi$
$677$	5.93746			0.228195			0.114098	+	0.993470i	$0.463602\pi$
$678$		0			0
$679$	−6.59366	−	11.4206i	−0.253041	−	0.438281i
$680$	−0.0233521	+	0.0404470i	−0.000895511	+	0.00155107i
$681$		0			0
$682$	1.14979	+	0.663829i	0.0440276	+	0.0254193i
$683$	26.7857	+	15.4648i	1.02493	+	0.591742i	0.915527	−	0.402255i	$-0.131774\pi$
$683$	26.7857	+	15.4648i	1.02493	+	0.591742i	0.109400	+	0.993998i	$0.465107\pi$
$684$		0			0
$685$	0.0605913	−	0.104947i	0.00231507	−	0.00400982i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	−0.998443			−0.0380653
$689$	−15.1573	−	10.5838i	−0.577448	−	0.403210i
$690$		0			0
$691$	−28.7071	+	16.5741i	−1.09207	+	0.630507i	−0.934127	−	0.356941i	$-0.883820\pi$
$691$	−28.7071	+	16.5741i	−1.09207	+	0.630507i	−0.157943	+	0.987448i	$0.550486\pi$
$692$	−9.43684	−	16.3451i	−0.358735	−	0.621347i
$693$		0			0
$694$		−	13.8194i		−	0.524576i
$695$	2.57690	+	1.48778i	0.0977475	+	0.0564345i
$696$		0			0
$697$		−	0.417995i		−	0.0158327i
$698$	−11.6775	+	20.2260i	−0.442000	+	0.765566i
$699$		0			0
$700$	−4.31179	+	2.48941i	−0.162970	+	0.0940910i
$701$	39.6504			1.49758			0.748788	−	0.662810i	$-0.230636\pi$
$701$	39.6504			1.49758			0.748788	+	0.662810i	$0.230636\pi$
$702$		0			0
$703$	−6.06816			−0.228865
$704$	1.30736	−	0.754806i	0.0492731	−	0.0284478i
$705$		0			0
$706$	9.75955	−	16.9040i	0.367305	−	0.636192i
$707$		−	15.3364i		−	0.576785i
$708$		0			0
$709$	27.3063	+	15.7653i	1.02551	+	0.592078i	0.915695	−	0.401875i	$-0.131641\pi$
$709$	27.3063	+	15.7653i	1.02551	+	0.592078i	0.109814	+	0.993952i	$0.464975\pi$
$710$			1.02603i			0.0385064i
$711$		0			0
$712$	4.11727	+	7.13132i	0.154301	+	0.267257i
$713$	−4.19285	+	2.42074i	−0.157024	+	0.0906576i
$714$		0			0
$715$	0.0679963	−	0.789070i	0.00254292	−	0.0295096i
$716$	17.9474			0.670727
$717$		0			0
$718$	15.5079	+	26.8604i	0.578749	+	1.00242i
$719$	11.4839	−	19.8908i	0.428279	−	0.741800i	−0.568442	−	0.822723i	$-0.692454\pi$
$719$	11.4839	−	19.8908i	0.428279	−	0.741800i	0.996720	+	0.0809233i	$0.0257869\pi$
$720$		0			0
$721$	1.82634	+	1.05444i	0.0680164	+	0.0392693i
$722$	14.0331	+	8.10199i	0.522256	+	0.301525i
$723$		0			0
$724$	5.01030	−	8.67809i	0.186206	−	0.322519i
$725$	22.8761	+	39.6225i	0.849596	+	1.47154i
$726$		0			0
$727$	−15.0527			−0.558275			−0.279138	−	0.960251i	$-0.590049\pi$
$727$	−15.0527			−0.558275			−0.279138	+	0.960251i	$0.590049\pi$
$728$	−3.26575	+	1.52804i	−0.121037	+	0.0566329i
$729$		0			0
$730$	−0.171017	+	0.0987369i	−0.00632964	+	0.00365442i
$731$	0.160237	+	0.277539i	0.00592659	+	0.0102651i
$732$		0			0
$733$		−	39.9321i		−	1.47493i	−0.675388	−	0.737463i	$-0.736024\pi$
$733$		−	39.9321i		−	1.47493i	0.675388	−	0.737463i	$-0.263976\pi$
$734$	−0.268496	−	0.155016i	−0.00991036	−	0.00572175i
$735$		0			0
$736$			5.50500i			0.202917i
$737$	−1.74128	+	3.01598i	−0.0641407	+	0.111095i
$738$		0			0
$739$	5.84273	−	3.37330i	0.214928	−	0.124089i	−0.388671	−	0.921376i	$-0.627066\pi$
$739$	5.84273	−	3.37330i	0.214928	−	0.124089i	0.603600	+	0.797287i	$0.293733\pi$
$740$	−0.528047			−0.0194114
$741$		0			0
$742$	5.12731			0.188229
$743$	−37.6905	+	21.7606i	−1.38273	+	0.798319i	−0.992482	−	0.122390i	$-0.960944\pi$
$743$	−37.6905	+	21.7606i	−1.38273	+	0.798319i	−0.390248	+	0.920710i	$0.627611\pi$
$744$		0			0
$745$	−0.995353	+	1.72400i	−0.0364669	+	0.0631625i
$746$			9.98856i			0.365707i
$747$		0			0
$748$	−0.419629	−	0.242273i	−0.0153432	−	0.00885838i
$749$			4.87216i			0.178025i
$750$		0			0
$751$	−1.52891	−	2.64814i	−0.0557906	−	0.0966322i	0.836781	−	0.547537i	$-0.184435\pi$
$751$	−1.52891	−	2.64814i	−0.0557906	−	0.0966322i	−0.892572	+	0.450905i	$0.851101\pi$
$752$	1.12742	−	0.650914i	0.0411126	−	0.0237364i
$753$		0			0
$754$	14.0417	+	30.0101i	0.511368	+	1.09290i
$755$	−0.0975938			−0.00355180
$756$		0			0
$757$	−8.76691	−	15.1847i	−0.318639	−	0.551899i	0.661565	−	0.749887i	$-0.269892\pi$
$757$	−8.76691	−	15.1847i	−0.318639	−	0.551899i	−0.980204	+	0.197989i	$0.936559\pi$
$758$	6.55010	−	11.3451i	0.237910	−	0.412073i
$759$		0			0
$760$	−0.210711	−	0.121654i	−0.00764328	−	0.00441285i
$761$	26.7397	+	15.4382i	0.969313	+	0.559633i	0.899027	−	0.437894i	$-0.144275\pi$
$761$	26.7397	+	15.4382i	0.969313	+	0.559633i	0.0702864	+	0.997527i	$0.477609\pi$
$762$		0			0
$763$	−5.20050	+	9.00753i	−0.188271	+	0.326094i
$764$	3.82269	+	6.62109i	0.138300	+	0.239543i
$765$		0			0
$766$	31.1154			1.12425
$767$	−4.91110	−	10.4961i	−0.177329	−	0.378991i
$768$		0			0
$769$	6.29237	−	3.63290i	0.226909	−	0.131006i	−0.382236	−	0.924065i	$-0.624846\pi$
$769$	6.29237	−	3.63290i	0.226909	−	0.131006i	0.609145	+	0.793059i	$0.291513\pi$
$770$	0.109830	+	0.190231i	0.00395799	+	0.00685545i
$771$		0			0
$772$		−	18.3171i		−	0.659247i
$773$	30.8223	+	17.7953i	1.10860	+	0.640051i	0.938467	−	0.345370i	$-0.112246\pi$
$773$	30.8223	+	17.7953i	1.10860	+	0.640051i	0.170134	+	0.985421i	$0.445580\pi$
$774$		0			0
$775$			4.37873i			0.157289i
$776$	−6.59366	+	11.4206i	−0.236699	+	0.409974i
$777$		0			0
$778$	7.64039	−	4.41118i	0.273921	−	0.158149i
$779$	2.17757			0.0780195
$780$		0			0
$781$	−10.6449			−0.380905
$782$	1.53024	−	0.883482i	0.0547211	−	0.0315932i
$783$		0			0
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$		−	1.27597i		−	0.0455415i
$786$		0			0
$787$	2.07853	+	1.20004i	0.0740914	+	0.0427767i	0.536588	−	0.843844i	$-0.319713\pi$
$787$	2.07853	+	1.20004i	0.0740914	+	0.0427767i	−0.462497	+	0.886621i	$0.653046\pi$
$788$			16.1442i			0.575115i
$789$		0			0
$790$	0.630205	+	1.09155i	0.0224217	+	0.0388355i
$791$	10.3014	−	5.94751i	0.366275	−	0.211469i
$792$		0			0
$793$	−10.7031	+	5.00796i	−0.380078	+	0.177838i
$794$	−8.56011			−0.303787
$795$		0			0
$796$	12.9703	+	22.4652i	0.459719	+	0.796257i
$797$	13.0250	−	22.5600i	0.461370	−	0.799117i	−0.537659	−	0.843162i	$-0.680691\pi$
$797$	13.0250	−	22.5600i	0.461370	−	0.799117i	0.999030	+	0.0440456i	$0.0140247\pi$
$798$		0			0
$799$	−0.361871	−	0.208926i	−0.0128021	−	0.00739129i
$800$	4.31179	+	2.48941i	0.152445	+	0.0880141i
$801$		0			0
$802$	−2.19937	+	3.80943i	−0.0776626	+	0.134516i
$803$	−1.02438	−	1.77427i	−0.0361494	−	0.0626127i
$804$		0			0
$805$	−0.801019			−0.0282322
$806$	−0.272243	+	3.15927i	−0.00958934	+	0.111280i
$807$		0			0
$808$	−13.2817	+	7.66821i	−0.467249	+	0.269767i
$809$	2.83859	+	4.91659i	0.0997996	+	0.172858i	0.911602	−	0.411075i	$-0.134846\pi$
$809$	2.83859	+	4.91659i	0.0997996	+	0.172858i	−0.811802	+	0.583933i	$0.801513\pi$
$810$		0			0
$811$			41.2139i			1.44722i	0.690211	+	0.723608i	$0.257518\pi$
$811$			41.2139i			1.44722i	−0.690211	+	0.723608i	$0.742482\pi$
$812$	−7.95821	−	4.59467i	−0.279278	−	0.161241i
$813$		0			0
$814$		−	5.47838i		−	0.192017i
$815$	0.675134	−	1.16937i	0.0236489	−	0.0409611i
$816$		0			0
$817$	−1.44585	+	0.834764i	−0.0505840	+	0.0292047i
$818$	16.5136			0.577384
$819$		0			0
$820$	0.189490			0.00661729
$821$	−16.7269	+	9.65729i	−0.583774	+	0.337042i	−0.762632	−	0.646833i	$-0.776093\pi$
$821$	−16.7269	+	9.65729i	−0.583774	+	0.337042i	0.178858	+	0.983875i	$0.442760\pi$
$822$		0			0
$823$	−18.2714	+	31.6470i	−0.636901	+	1.10314i	0.349208	+	0.937045i	$0.386451\pi$
$823$	−18.2714	+	31.6470i	−0.636901	+	1.10314i	−0.986109	+	0.166099i	$0.946883\pi$
$824$		−	2.10888i		−	0.0734662i
$825$		0			0
$826$	2.78339	+	1.60699i	0.0968467	+	0.0559145i
$827$			10.4134i			0.362108i	0.983473	+	0.181054i	$0.0579509\pi$
$827$			10.4134i			0.362108i	−0.983473	+	0.181054i	$0.942049\pi$
$828$		0			0
$829$	−20.2110	−	35.0066i	−0.701959	−	1.21583i	−0.967778	−	0.251805i	$-0.918976\pi$
$829$	−20.2110	−	35.0066i	−0.701959	−	1.21583i	0.265819	−	0.964023i	$-0.414358\pi$
$830$	−0.0187205	+	0.0108083i	−0.000649797	+	0.000375160i
$831$		0			0
$832$	2.95619	+	2.06420i	0.102488	+	0.0715633i
$833$	−0.320974			−0.0111211
$834$		0			0
$835$	0.340971	+	0.590580i	0.0117998	+	0.0204378i
$836$	1.26213	−	2.18608i	0.0436518	−	0.0756072i
$837$		0			0
$838$	28.5753	+	16.4980i	0.987119	+	0.569913i
$839$	45.3995	+	26.2114i	1.56736	+	0.904918i	0.996475	+	0.0838897i	$0.0267343\pi$
$839$	45.3995	+	26.2114i	1.56736	+	0.904918i	0.570888	+	0.821028i	$0.306599\pi$
$840$		0			0
$841$	−27.7220	+	48.0160i	−0.955932	+	1.65572i
$842$	−0.836556	−	1.44896i	−0.0288296	−	0.0499344i
$843$		0			0
$844$	10.0438			0.345721
$845$	1.77582	−	0.651605i	0.0610902	−	0.0224159i
$846$		0			0
$847$	7.55267	−	4.36054i	0.259513	−	0.149830i
$848$	−2.56366	−	4.44038i	−0.0880363	−	0.152483i
$849$		0			0
$850$		−	1.59807i		−	0.0548135i
$851$	17.3012	+	9.98883i	0.593076	+	0.342413i
$852$		0			0
$853$		−	33.2052i		−	1.13692i	−0.822709	−	0.568462i	$-0.807539\pi$
$853$		−	33.2052i		−	1.13692i	0.822709	−	0.568462i	$-0.192461\pi$
$854$	1.63869	−	2.83829i	0.0560748	−	0.0971243i
$855$		0			0
$856$	4.21941	−	2.43608i	0.144217	−	0.0832635i
$857$	−7.65504			−0.261491			−0.130746	−	0.991416i	$-0.541737\pi$
$857$	−7.65504			−0.261491			−0.130746	+	0.991416i	$0.541737\pi$
$858$		0			0
$859$	−17.1318			−0.584528			−0.292264	−	0.956338i	$-0.594409\pi$
$859$	−17.1318			−0.584528			−0.292264	+	0.956338i	$0.594409\pi$
$860$	−0.125817	+	0.0726405i	−0.00429032	+	0.00247702i
$861$		0			0
$862$	3.26026	−	5.64693i	0.111045	−	0.192335i
$863$		−	35.0912i		−	1.19452i	−0.802049	−	0.597259i	$-0.796257\pi$
$863$		−	35.0912i		−	1.19452i	0.802049	−	0.597259i	$-0.203743\pi$
$864$		0			0
$865$	−2.37833	−	1.37313i	−0.0808657	−	0.0466878i
$866$		−	0.0257034i		−	0.000873437i
$867$		0			0
$868$	−0.439735	−	0.761644i	−0.0149256	−	0.0258519i
$869$	−11.3246	+	6.53825i	−0.384160	+	0.221795i
$870$		0			0
$871$	−8.28700	−	0.714114i	−0.280794	−	0.0241968i
$872$	10.4010			0.352222
$873$		0			0
$874$	4.60254	+	7.97184i	0.155683	+	0.269651i
$875$	−0.725997	+	1.25746i	−0.0245432	+	0.0425100i
$876$		0			0
$877$	23.0035	+	13.2811i	0.776773	+	0.448470i	0.835285	−	0.549817i	$-0.185302\pi$
$877$	23.0035	+	13.2811i	0.776773	+	0.448470i	−0.0585126	+	0.998287i	$0.518636\pi$
$878$	26.1509	+	15.0983i	0.882551	+	0.509541i
$879$		0			0
$880$	0.109830	−	0.190231i	0.00370236	−	0.00641268i
$881$	25.3323	+	43.8768i	0.853466	+	1.47825i	0.878061	+	0.478550i	$0.158837\pi$
$881$	25.3323	+	43.8768i	0.853466	+	1.47825i	−0.0245942	+	0.999698i	$0.507829\pi$
$882$		0			0
$883$	−10.9125			−0.367235			−0.183618	−	0.982998i	$-0.558781\pi$
$883$	−10.9125			−0.367235			−0.183618	+	0.982998i	$0.558781\pi$
$884$	0.0993585	−	1.15302i	0.00334179	−	0.0387801i
$885$		0			0
$886$	−18.5381	+	10.7030i	−0.622799	+	0.359573i
$887$	−7.49249	−	12.9774i	−0.251573	−	0.435738i	0.712386	−	0.701788i	$-0.247615\pi$
$887$	−7.49249	−	12.9774i	−0.251573	−	0.435738i	−0.963959	+	0.266050i	$0.914281\pi$
$888$		0			0
$889$		−	6.17664i		−	0.207158i
$890$	1.03766	+	0.599094i	0.0347825	+	0.0200817i
$891$		0			0
$892$			8.53615i			0.285811i
$893$	1.08841	−	1.88519i	0.0364224	−	0.0630854i
$894$		0			0
$895$	2.26161	−	1.30574i	0.0755974	−	0.0436462i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−30.4522			−1.01620
$899$	−6.99901	+	4.04088i	−0.233430	+	0.134771i
$900$		0			0
$901$	−0.822867	+	1.42525i	−0.0274137	+	0.0474819i
$902$			1.96592i			0.0654581i
$903$		0			0
$904$	−10.3014	−	5.94751i	−0.342619	−	0.197811i
$905$		−	1.45807i		−	0.0484679i
$906$		0			0
$907$	2.89845	+	5.02027i	0.0962415	+	0.166695i	0.910126	−	0.414331i	$-0.135985\pi$
$907$	2.89845	+	5.02027i	0.0962415	+	0.166695i	−0.813885	+	0.581027i	$0.802651\pi$
$908$	−8.65098	+	4.99464i	−0.287093	+	0.165753i
$909$		0			0
$910$	−0.300357	+	0.430148i	−0.00995672	+	0.0142593i
$911$	45.1175			1.49481			0.747405	−	0.664369i	$-0.231300\pi$
$911$	45.1175			1.49481			0.747405	+	0.664369i	$0.231300\pi$
$912$		0			0
$913$	−0.112134	−	0.194221i	−0.00371108	−	0.00642778i
$914$	−6.29450	+	10.9024i	−0.208203	+	0.360619i
$915$		0			0
$916$	−15.7145	−	9.07275i	−0.519221	−	0.299772i
$917$	3.13489	+	1.80993i	0.103523	+	0.0597691i
$918$		0			0
$919$	−18.1331	+	31.4075i	−0.598157	+	1.03604i	0.394936	+	0.918708i	$0.370767\pi$
$919$	−18.1331	+	31.4075i	−0.598157	+	1.03604i	−0.993093	+	0.117329i	$0.962567\pi$
$920$	0.400510	+	0.693703i	0.0132044	+	0.0228707i
$921$		0			0
$922$	11.0205			0.362940
$923$	−10.7748	−	23.0282i	−0.354658	−	0.757981i
$924$		0			0
$925$	15.6475	−	9.03409i	0.514486	−	0.297039i
$926$	0.689170	+	1.19368i	0.0226475	+	0.0392267i
$927$		0			0
$928$			9.18935i			0.301655i
$929$	−35.1857	−	20.3145i	−1.15440	−	0.666496i	−0.204448	−	0.978877i	$-0.565540\pi$
$929$	−35.1857	−	20.3145i	−1.15440	−	0.666496i	−0.949957	+	0.312381i	$0.898873\pi$
$930$		0			0
$931$		−	1.67213i		−	0.0548019i
$932$	1.79425	−	3.10774i	0.0587727	−	0.101797i
$933$		0			0
$934$	−15.8454	+	9.14837i	−0.518478	+	0.299344i
$935$	−0.0705051			−0.00230576
$936$		0			0
$937$	42.0408			1.37341			0.686707	−	0.726934i	$-0.259056\pi$
$937$	42.0408			1.37341			0.686707	+	0.726934i	$0.259056\pi$
$938$	1.99785	−	1.15346i	0.0652321	−	0.0376618i
$939$		0			0
$940$	0.0947128	−	0.164047i	0.00308919	−	0.00535064i
$941$			31.8484i			1.03823i	0.854705	+	0.519114i	$0.173738\pi$
$941$			31.8484i			1.03823i	−0.854705	+	0.519114i	$0.826262\pi$
$942$		0			0
$943$	−6.20854	−	3.58450i	−0.202178	−	0.116728i
$944$		−	3.21399i		−	0.104606i
$945$		0			0
$946$	−0.753631	−	1.30533i	−0.0245026	−	0.0424398i
$947$	23.8646	−	13.7782i	0.775495	−	0.447732i	−0.0593364	−	0.998238i	$-0.518898\pi$
$947$	23.8646	−	13.7782i	0.775495	−	0.447732i	0.834831	+	0.550506i	$0.185565\pi$
$948$		0			0
$949$	2.80141	−	4.01196i	0.0909375	−	0.130234i
$950$	8.32525			0.270107
$951$		0			0
$952$	0.160487	+	0.277972i	0.00520142	+	0.00900912i
$953$	−14.2985	+	24.7658i	−0.463175	+	0.802243i	−0.999117	−	0.0420117i	$-0.986623\pi$
$953$	−14.2985	+	24.7658i	−0.463175	+	0.802243i	0.535942	+	0.844255i	$0.319957\pi$
$954$		0			0
$955$	0.963418	+	0.556230i	0.0311755	+	0.0179992i
$956$	10.4402	+	6.02766i	0.337661	+	0.194949i
$957$		0			0
$958$	13.5748	−	23.5123i	0.438582	−	0.759647i
$959$	−0.416413	−	0.721249i	−0.0134467	−	0.0232903i
$960$		0			0
$961$	30.2265			0.975049
$962$	11.8514	−	5.54525i	0.382104	−	0.178786i
$963$		0			0
$964$	9.68612	−	5.59229i	0.311969	−	0.180115i
$965$	−1.33264	−	2.30820i	−0.0428991	−	0.0743034i
$966$		0			0
$967$			17.4799i			0.562115i	0.959691	+	0.281057i	$0.0906851\pi$
$967$			17.4799i			0.562115i	−0.959691	+	0.281057i	$0.909315\pi$
$968$	−7.55267	−	4.36054i	−0.242752	−	0.140153i
$969$		0			0
$970$			1.91885i			0.0616107i
$971$	−14.5288	+	25.1646i	−0.466251	+	0.807570i	−0.999257	−	0.0385416i	$-0.987729\pi$
$971$	−14.5288	+	25.1646i	−0.466251	+	0.807570i	0.533006	+	0.846111i	$0.321062\pi$
$972$		0			0
$973$	17.7098	−	10.2247i	0.567749	−	0.327790i
$974$	20.8436			0.667872
$975$		0			0
$976$	−3.27738			−0.104906
$977$	−22.6162	+	13.0575i	−0.723556	+	0.417745i	−0.816060	−	0.577967i	$-0.803846\pi$
$977$	−22.6162	+	13.0575i	−0.723556	+	0.417745i	0.0925039	+	0.995712i	$0.470513\pi$
$978$		0			0
$979$	−6.21548	+	10.7655i	−0.198647	+	0.344068i
$980$		−	0.145508i		−	0.00464807i
$981$		0			0
$982$	−21.3438	−	12.3228i	−0.681108	−	0.393238i
$983$			10.0398i			0.320219i	0.987099	+	0.160109i	$0.0511847\pi$
$983$			10.0398i			0.320219i	−0.987099	+	0.160109i	$0.948815\pi$
$984$		0			0
$985$	1.17455	+	2.03439i	0.0374244	+	0.0648209i
$986$	2.55438	−	1.47477i	0.0813480	−	0.0469663i
$987$		0			0
$988$	6.00669	+	0.517613i	0.191098	+	0.0164675i
$989$	5.49643			0.174776
$990$		0			0
$991$	6.78355	+	11.7494i	0.215486	+	0.373234i	0.953423	−	0.301637i	$-0.0975329\pi$
$991$	6.78355	+	11.7494i	0.215486	+	0.373234i	−0.737936	+	0.674870i	$0.764200\pi$
$992$	−0.439735	+	0.761644i	−0.0139616	+	0.0241822i
$993$		0			0
$994$	6.10671	+	3.52571i	0.193693	+	0.111829i
$995$	3.26885	+	1.88727i	0.103630	+	0.0598306i
$996$		0			0
$997$	30.7329	−	53.2310i	0.973321	−	1.68584i	0.287952	−	0.957645i	$-0.407026\pi$
$997$	30.7329	−	53.2310i	0.973321	−	1.68584i	0.685368	−	0.728196i	$-0.259641\pi$
$998$	0.522220	+	0.904512i	0.0165306	+	0.0286318i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.i.127.3	yes	16
3.2	odd	2		1638.2.bj.h.127.6	✓	16
13.4	even	6	inner	1638.2.bj.i.1135.2	yes	16
39.17	odd	6		1638.2.bj.h.1135.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bj.h.127.6	✓	16	3.2	odd	2
1638.2.bj.h.1135.7	yes	16	39.17	odd	6
1638.2.bj.i.127.3	yes	16	1.1	even	1	trivial
1638.2.bj.i.1135.2	yes	16	13.4	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -0.145508i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -0.145508i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(0.0727538 + 0.126013i) q^{10} +(-1.30736 + 0.754806i) q^{11} +(-2.95619 - 2.06420i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.160487 + 0.277972i) q^{17} +(-1.44811 - 0.836065i) q^{19} +(-0.126013 - 0.0727538i) q^{20} +(0.754806 - 1.30736i) q^{22} +(2.75250 + 4.76747i) q^{23} +4.97883 q^{25} +(3.59224 + 0.309553i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(4.59467 + 7.95821i) q^{29} +0.879471i q^{31} +(0.866025 + 0.500000i) q^{32} -0.320974i q^{34} +(-0.0727538 + 0.126013i) q^{35} +(3.14281 - 1.81450i) q^{37} +1.67213 q^{38} +0.145508 q^{40} +(-1.12780 + 0.651136i) q^{41} +(0.499222 - 0.864677i) q^{43} +1.50961i q^{44} +(-4.76747 - 2.75250i) q^{46} +1.30183i q^{47} +(0.500000 + 0.866025i) q^{49} +(-4.31179 + 2.48941i) q^{50} +(-3.26575 + 1.52804i) q^{52} +5.12731 q^{53} +(0.109830 + 0.190231i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-7.95821 - 4.59467i) q^{58} +(2.78339 + 1.60699i) q^{59} +(1.63869 - 2.83829i) q^{61} +(-0.439735 - 0.761644i) q^{62} -1.00000 q^{64} +(-0.300357 + 0.430148i) q^{65} +(1.99785 - 1.15346i) q^{67} +(0.160487 + 0.277972i) q^{68} -0.145508i q^{70} +(6.10671 + 3.52571i) q^{71} +1.35714i q^{73} +(-1.81450 + 3.14281i) q^{74} +(-1.44811 + 0.836065i) q^{76} +1.50961 q^{77} +8.66217 q^{79} +(-0.126013 + 0.0727538i) q^{80} +(0.651136 - 1.12780i) q^{82} +0.148560i q^{83} +(0.0404470 + 0.0233521i) q^{85} +0.998443i q^{86} +(-0.754806 - 1.30736i) q^{88} +(7.13132 - 4.11727i) q^{89} +(1.52804 + 3.26575i) q^{91} +5.50500 q^{92} +(-0.650914 - 1.12742i) q^{94} +(-0.121654 + 0.210711i) q^{95} +(11.4206 + 6.59366i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 2 q^{10} + 12 q^{11} + 10 q^{13} + 16 q^{14} - 8 q^{16} + 6 q^{17} - 4 q^{22} + 12 q^{23} - 20 q^{25} + 2 q^{26} - 16 q^{29} - 2 q^{35} - 6 q^{37} + 4 q^{40} - 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} + 24 q^{50} - 4 q^{52} + 40 q^{53} + 20 q^{55} + 8 q^{56} + 6 q^{58} - 6 q^{59} - 2 q^{61} + 14 q^{62} - 16 q^{64} + 52 q^{65} - 30 q^{67} - 6 q^{68} - 12 q^{71} - 24 q^{74} - 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} - 30 q^{89} + 4 q^{91} + 24 q^{92} - 8 q^{94} + 40 q^{95} - 24 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^10 + 12 * q^11 + 10 * q^13 + 16 * q^14 - 8 * q^16 + 6 * q^17 - 4 * q^22 + 12 * q^23 - 20 * q^25 + 2 * q^26 - 16 * q^29 - 2 * q^35 - 6 * q^37 + 4 * q^40 - 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 + 24 * q^50 - 4 * q^52 + 40 * q^53 + 20 * q^55 + 8 * q^56 + 6 * q^58 - 6 * q^59 - 2 * q^61 + 14 * q^62 - 16 * q^64 + 52 * q^65 - 30 * q^67 - 6 * q^68 - 12 * q^71 - 24 * q^74 - 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 - 30 * q^89 + 4 * q^91 + 24 * q^92 - 8 * q^94 + 40 * q^95 - 24 * q^97

Introduction

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